Ronald Jones

Attribute Openings, Thinnings, and Granulometries

In this paper we establish an attribute-based approach to openings and closings and provide an efficient algorithm for their implementation on gray-scale images. Attribute openings are similar to openings by reconstruction since they are connected component transformations. However, attribute openings are more general because they can describe generalized shape features and openings that have no shape-bias. This work is then extended to gray-scale granuolmetries and to include gray-scale thinnings, which are nonincreasing filters. The use of nonincreasing gray-scale thinnings is seen as an important generalization because it allows the use of nonincreasing shape descriptors such as compactness and eccentricity to be applied to filter gray-scale images. Applications are then given to illustrate the performance of the filters proposed.

Connected Filtering and Segmentation Using Component Trees

This paper formalizes the notion of nonflat gray-level connected filters and proposes efficient algorithms for their implementation in a supplementary web page. The component tree is proposed as an efficient and accessible data structure used to implement these filters. The primary nonflat component filter advocated in this paper is based on the concept of an attribute signature. The attribute signature captures both attribute and linking information between components in a gray-level image and can be a powerful means of discriminating desired image features. One of the key benefits of the approach is that the image features to be filtered undergo the maximum amount of filtering that is possible without altering the rest of the image at all. As a consequence, an image segmentation can be obtained simply by finding those pixels within the image that have been changed by the filter. We present an application of nonflat component filters to the segmentation of wood micrographs.

Recursive implementation of erosions and dilations along discrete lines at arbitrary angles

Van Herk (1992) has shown that the erosion/dilation operator with a linear structuring element of an arbitrary length can be implemented in only three min/max operations per pixel. In this paper, the algorithm is generalized to erosions and dilations along discrete lines at arbitrary angles. We also address the padding problem; so that the operation can be performed in place without copying the pixels to and from an intermediate buffer. Applications to image filtering and to radial decompositions of discs are presented.

Periodic lines: Definition, cascades, and application to granulometries

In this paper we introduce the notion of periodic lines. In contrast to other types of lines such as Bresenham lines, periodic lines can be used to generate a wide range of granulometric functions via structural decomposition.

Segmenting multispectral Landsat TM images into field units

Presents a procedure for the automated segmentation of multispectral Landsat TM images of farmland in Western Australia into field units. The segmentation procedure, named the canonically-guided region growing (CGRG) procedure, assumes that each field contains only one ground cover type and that the width of the minimum field of interest is known. The CGRG procedure segments images using a seeded region growing algorithm, but is novel in the method used to generate the internal field markers used as seeds. These internal field markers are obtained from a multiband, local canonical eigenvalue image. Before the local transformation is applied, the original image is morphologically filtered to estimate both between-field variation and within-field variation in the image. Local computation of the canonical variate transform, using a moving window sized to fit just inside the smallest field of interest, ensures that the between- and within-field spatial variations in each image band are accommodated. The eigenvalues of the local transform are then used to discriminate between an area completely inside a field or at a field boundary. The results obtained using CGRG and the methods of Lee (1997) and Tilton (1998) were numerically compared to ideal segmentations of a set of sample satellite images. The comparison indicates that the results of the CGRG are usually more accurate in terms of field boundary position and degree of over-segmentation and under-segmentation, than either of the other procedures.

Fast computation of moving average and related filters in octagonal windows

Abstract A method is proposed for efficiently computing moving average filters in regular octagonal windows, as approximations to circular windows. The algorithm requires thirteen operations per pixel irrespective of window size and is faster than existing Fourier-based and recursive methods for all but the smallest windows. Further, new variance-weighted nonlinear filters are introduced, based on moving average filters. They are shown to smooth speckly images more effectively than existing filters.

Mathematical morphology: A useful set of tools for imageanalysis

In this paper we give an overview of both classical and more modern morphological techniques. We will demonstrate their utility through a range of practical examples. After discussing the fundamental morphological ideas, we show how the classic morphological opening and closing filters lead to measures of size via granulometries, and we will discuss briefly their implementation. We also present an overview of morphological segmentation techniques, and the use of connected openings and thinnings will be demonstrated. This then leads us into the more recent set-theoretic notions of graph based approaches to image analysis.

Periodic Lines and their Application to Granulometries

In this paper we introduce the notion of periodic lines. In contrast to other types of digital lines such as Bresenham lines, periodic lines can be used to generate a wide range of granulometric functions via structural decomposition.